you know that 8x = 5y
you know that 3y=14z
since 5 = (5/3)*3, 5y = (5/3)*(3y) so,
5y = (5/3)(3y) = (5/3)(14z) = (70/3)z
now you have 5y, which is the same as 8x. You want 12x.
since 12 = (3/2)*8, 12x = (3/2)*8x.
12x = (3/2)(8x) = (3/2)(5y) = (3/2)(70/3)z = (70/2)z = 35z
Can you step in and help me understand where you got (3/2) in the second expression
helps to read:
since 12 = (3/2)*8
Sure! In the second expression, we have 12x. We want to find a relationship between 12x and 8x, so we can manipulate the equation using the idea of equivalent fractions.
We know that 12 = (3/2) * 8. This means that if we multiply 8x by (3/2), we will get 12x. Mathematically, we have:
12x = (3/2) * 8x
To understand where we got (3/2), we can break it down as follows:
Since we know that 12 = (3/2) * 8, we can divide both sides by 8 to isolate (3/2):
12 / 8 = (3/2) * (8 / 8)
Reducing the fraction on the right-hand side, we get:
12 / 8 = (3/2) * 1
Simplifying further, we have:
3/2 = (3/2) * 1
So, the (3/2) comes from the idea that dividing 12 by 8 gives us (3/2).
Now, substituting this value back into our equation, we have:
12x = (3/2) * 8x
which simplifies to:
12x = (3/2) * 8x
Therefore, in the given context, (3/2) comes from the proportionality between 12 and 8 in order to find the relationship between 12x and 8x.